A school board decides that it is worth adopting a new method of instruction if it improves performance on a final exam by at least 8 marks. In an experiment designed to compare the new method with the traditional one, students are to be assigned randomly to one of the two methods.

1. Given an estimate of 12 marks as the standard deviation of final exam scores, how many students are needed in each group to ensure a 95% confidence interval with a half-width w of 5 marks? Round UP to the nearest whole number.

Question

A school board decides that it is worth adopting a new method of instruction if it improves performance on a final exam by at least 8 marks. In an experiment designed to compare the new method with the traditional one, students are to be assigned randomly to one of the two methods.
 
1. Given an estimate of 12 marks as the standard deviation of final exam scores, how many students are needed in each group to ensure a 95% confidence interval with a half-width w of 5 marks? Round UP to the nearest whole number.